From the point of view of the Sun, some satellites with short orbital periods might appear to move back and forth as they run around their planet. Earth's Moon, on the other hand, never moves backward from the point of view of the Sun.
That still wouldn't make the Moon a planet though.
the orbital period of the satellite isn't as important as the orbital velocity of the planet around the sun.
the earth goes around the sun at 29 785.8944 mps, so for a satellite to appear to stand still (from the sun's perspective) it needs that orbital speed (i'm assuming that everything orbits in the same plane to make things easier/cleaner).
using the equation v^2 = GM/R gives an orbital radius of(G = 6.673 x 10^-11 N m^2/kg^2 and M = 5.98x10^24 kg, 1N = 1kg * 1m /1s) 449, 777 m or 449.7 km. Of course, the radius of the earth is 6.3 million meters (6300 km), so this isn't exactly possible.
the only way for a satellite orbiting a planet to appear to move backwards with respect to the thing the planet orbits is for the satellite to have a faster orbital velocity than the planet's orbital velocity.
That still wouldn't make the Moon a planet though.